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Some characterizations of the Euclidean rectifying curves, i.e. the curves in E 3 which have a property that their position vector always lies in their rectifying plane, are given in . In this paper, we characterize non–null and null rectifying curves, lying fully in the Minkowski 3–space E 3 1. Also, in considering a causal character of a curve we give… (More)
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We define pseudohyperbolical Smarandache curves according to the Sabban frame in Minkowski 3-space. We obtain the geodesic curvatures and the expression for the Sabban frame vectors of special pseudohyperbolic Smarandache… (More)
In this paper, we characterize the spacelike, the timelike and the null rectifying curves in the Minkowski 3-space in terms of centrodes. In particular, we show that the spacelike and timelike rectifying curves are the extremal curves for which the corresponding function takes its extremal value. On the other hand, we also show that the null rectifying… (More)
In this paper, we define Mannheim partner curves in three dimensional dual space D 3 and we obtain the necessary and sufficient conditions for the Mannheim partner curves in dual space D 3 .
In this study, we have investigated the possibility of whether any Frenet plane of a given space curve in a 3-dimensional Euclidean space E 3 also is any Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.